The phrase 'With this brief' is perfectly correct and usable in written English.
It generally refers to accompanying a statement or comment with a brief explanation. For example: "I cannot tell you the full story, but with this brief I will explain what I can."
"With this brief visit," he said, "I wish to greet all Mexicans and to include all the people of Latin America, represented here by many bishops".
With this brief correspondence we would like to recapitulate four important aspects of scientific research practice, which should be taken into consideration as early as possible in the course of any project.
When I was tasked with this brief, I was reminded of an American art project, In search of the truth.
While you're waiting, start with this brief history of the MP3 written by Eric Harvey for Pitchfork.
Now the comedian, feted by Variety and Rolling Stone, has another chance to shine with this brief London residency.
Already one of the most fascinating figures in the history of popular fiction, JK Rowling has become even more intriguing with this brief but neat vanishing trick.
Choreographed in collaboration with Christopher Huggins, this brief but feisty exercise in shimmying and attitude was performed with Kim Bears-Bailey, Philadanco's assistant artistic director.
In a city where even the great parks are jammed with traffic, this brief period of freedom and tranquillity was nothing short of exhilarating.
Dazzlingly shot and spiked with tender ironies, this brief encounter between romance and sociology confirms its star Valeria Bruni-Tedeschi as one of the current names to watch.
Familiarize yourself with the system via this brief video.
And yet, with this relatively brief exposure to hazard, one-third of them will end up with dementia or some other brain disease.
